Question

For the month of January in a certain​ city, 42​% of the days are cloudy. Also in the month of January in the same​ city, 41​% of the days are cloudy and rainy. What is the probability that a randomly selected day in January will be rainy if it is cloudy​?

Answer 1

Answer: 0.9762

Step-by-step explanation:

Let A be the event that days are cloudy and B be the event that days are rainy for January month .

Given : The probability that the days are cloudy = $P(A)=0.42$

The probability that the days are cloudy and rainy = $P(A\cap B)=0.41$

Now, the conditional probability that a randomly selected day in January will be rainy if it is cloudy is given by :-

$P(B|A)=\dfrac{P(B\cap A)}{P(A)}\\\\\Rightarrow\ P(B|A)=\dfrac{0.41}{0.42}=0.97619047619\approx0.9762$

Hence, the probability that a randomly selected day in January will be rainy if it is cloudy  = 0.9762